Blender Internals to EEVEE?
Before 2.8 there was addons to convert Blender Internal materials into Cycles materials.
But in 2.8 none of those addons have been upgraded to the new addon API changes yet. You could wait until one is upgraded.

In the meantime, you can simply make yourself a separate installation of Blender 2.79 and use its integrated Material Utils addon to convert your Internal materials into Cycles.
Then append the Cycles material into your 2.8 scene. Cycles materials are mostly compatible with Eevee, so there shouldn't be much issues switching from Cycles to Eevee.